In integrated optic wavelength division multiplexed (WDM) communication systems, designing a grating structure for a desired grating strength is a significant concern. Obtaining a desired grating strength typically requires the control of a number of grating design parameters, resulting in numerous design tradeoffs. These numerous parameters must also be precisely controlled during the fabrication process, often resulting in low yields.
Electromagnetic waveguides may have periodic structures, called gratings, introduced into them. A typical grated waveguide containing a grating is shown in FIG. 1. Waveguides containing such periodic structures are termed grated waveguides. A grated waveguide can be characterized by an effective index, neff, and a grating strength, κ, for each electromagnetic mode that propagates through the grated waveguide. The grating shape can be described by a period, Λ, and the dimensions of the periodic features, or “teeth”.
Most gratings are designed by adjusting the shape and dielectric constants of the grated waveguide to simultaneously obtain a desired grating strength and effective index for each mode in the grated waveguide. Typically each of these parameters needs to meet a target specification to high precision.
A grated waveguide couples light between propagating modes, and is typically used to reflect or transmit light over an optical frequency band, or “bandgap”, or “stopband”, which is proportional to κ. The stopband width, or bandgap, Δω, is related to κ as                               Δ          ⁢                                          ⁢          ω                =                              2            ⁢            c            ⁢                                                  ⁢            κ                                n            g                                              (        1        )            where ng is the modal group index and c is the speed of light. The frequency at the middle of the stopband is called the center frequency. The center radian frequency, ωc, of the stopband and the coupling order, q, are related to the effective index, neff, and the period, Λ, as                               ω          c                =                                            2              ⁢              π              ⁢                                                          ⁢              cq                                      n              eff                                ⁢                                    1              Λ                        .                                              (        2        )            
A common application of a grating is to reflect light from the forward propagating mode to a backward propagating mode in a waveguide, such as in frequency filters, distributed Bragg reflector (DBR) laser cavities, and resonator cavities.
In integrated optical devices containing gratings, it is often desirable to have a variety of grated waveguides with differing strengths produced during the same fabrication process. Errors and fluctuations in the fabrication process make it difficult to obtain precise grating properties. Differences in these fabrication errors and fluctuations for the various grated waveguides on the device also make it difficult to precisely match the properties of the various gratings.
Additionally, in the design process, multiple design constraints must be simultaneously satisfied. Consequently, the design process is often complicated by the interdependencies of the design parameters, and a complex multivariable optimization is required.
One application in which a wide range of grating strengths are required, while the other grating properties are maintained to a high precision, is apodization. Apodization is the variation of the grating strength along the length of the gating so that, for example, the grating has a tapered grating strength and the spectral response of the grating is improved.
Previous grating design processes involve adjusting the shape parameters and dielectric constants of the grated waveguide, such as duty cycle and tooth depth, to simultaneously attain design criteria. One method of obtaining a desired grating strength is to adjust the duty cycle of the periodic structure. Alternatively, the tooth depth can be adjusted to obtain a desired grating strength for a single polarization mode. In many commercial applications, the modes of interest are the two polarization states of the lowest order spatial mode, or the “polarization modes”. Apodized gratings with similar properties for the two polarization modes have been fabricated in grated waveguides by designing the tooth shape for each desired grating strength.
However, because the design parameters are interdependent, design flexibility can be significantly limited. In addition, because of these parameter interdependencies, some desired design criteria may not be achievable. Furthermore, these methods are sensitive to fabrication errors and fluctuations.
By adjusting the duty cycle of the grating teeth, the grating strength is engineered. However, the grating period must be simultaneously adjusted to compensate for the large effect of the duty cycle on the effective index. Alternatively, by adjusting the tooth depth of the grating, the target grating strength of one polarization can be attained. However, the cross section of the waveguide must be simultaneously adjusted to compensate for the effect of the adjusted tooth depth on the effective index of the grating. Typically, the optical properties of the other polarization modes are detrimentally affected. Fabrication errors and fluctuations can also degrade this compensation scheme.
In polarization controlled gratings that use various tooth shapes to achieve the range of grating strengths required for apodization, the fabrication difficulty increases. Typically, a fabrication process is optimized to produce a specific grating shape. When multiple shapes must be simultaneously fabricated, compromises, such as shape approximation, are inevitable, and fabrication fidelity is reduced. In addition, fabrication errors are manifested differently for the various shapes, resulting in unmatched errors. In apodization applications the tolerances on the matching of parameters are extremely tight and the fabrication errors result in even greater variations. The design complexity also increases because a complicated multivariable optimization must be performed for each grating strength.